*Title*: **Quantum Differential Equations**

*Abstract*:For a smooth variety X, Gromov-Witten invariants of X are used to define a deformation of the cup product in the cohomology of X known as the quantum product.
The quantum differential equation for X is a system of (partial) differential equations that encodes the structures of quantum cup product of X.
In this talk we will describe the construction of quantum cup product and quantum differential equations.
We will also discuss some analytic properties of the quantum differential equations for some spaces X, such as the projective space and the Hilbert schemes of points in the plane.

CAM Seminar Fall 2017 - Spring 2018